一种加权抛物Radon变换地震波场重建方法
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摘要
基于带限正反抛物Radon变换的基本原理和计算方法,笔者给出了一种加权抛物Radon变换(PRT)算法,该方法可应用于叠前地震波场恢复和重建,如缺失偏移距地震数据的插值外推和反假频重采样,其权系数完全由数据域来确定,也就是说在迭代计算过程中,该权系数也在变化。对于均匀采样的地震数据,笔者给出了近偏移距外推和波场的反假频重采样的计算结果,试算表明笔者给出的加权PRT方法可有效地应用于地震波场重建中,并具有算法稳健、计算精度高和效率高的特点。
A weighted parabolic Radon transform approach is proposed based on the basic principle and computation method of conventional band-limited forward and inverse parabolic radon transform.The proposed algorithm is applied to prestack seismic wavefield restoration and reconstruction,such as the missing offset interpolation and anti-alias resampling in the offset direction;The weight coefficient is determined by seismic data in x-τ domain,i.e.,the weight coefficient varies in different iteration processes.For the seismic data from uniform sampling,this paper gives the reconstruction result of missing near offset extrapolation and resampling for anti-alias seismic data.The test results demonstrate that the presented weighted parabolic radon transform is effective for seismic wavefield reconstruction,with the characteristics of robustness,high precision and high efficiency.
A weighted parabolic Radon transform approach is proposed based on the basic principle and computation method of conventional band-limited forward and inverse parabolic radon transform.The proposed algorithm is applied to prestack seismic wavefield restoration and reconstruction,such as the missing offset interpolation and anti-alias resampling in the offset direction;The weight coefficient is determined by seismic data in x-τ domain,i.e.,the weight coefficient varies in different iteration processes.For the seismic data from uniform sampling,this paper gives the reconstruction result of missing near offset extrapolation and resampling for anti-alias seismic data.The test results demonstrate that the presented weighted parabolic radon transform is effective for seismic wavefield reconstruction,with the characteristics of robustness,high precision and high efficiency.
引文
[1]Verschuur D J.Surface-related multiple elimination,an inversionapproach[D].Delft University of Technology,1991.
[2]Kabir M M N,Verschuur D J.Restoration of missing offsets by par-abolic Radon Transform[J].Geophysical Prospecting,1995,43:347-368.
[3]黄新武,吴律,牛滨华.基于抛物线拉东变换的地震道重构[J].中国矿业大学学报,2003,32(5):534-539.
[4]王维红,裴江云,张剑锋.加权抛物Radon变换叠前地震数据重建[J].地球物理学报,2007,50(3):851-859.
[5]Hampson D.Inverse velocity stacking for multiple elimination[J].Journal of the Canadian Society of Exploration geophysicists,1986,22:44-55.
[6]Kostov C.Toeplitz structure in slant-stack inversion:60th AnnualInternat[C]//60th Annual Internat Mtg Soc Expl Geophys,Ex-panded abstracts,1990:1618-1621.
[7]Trad D,Ulrych J,Sacchi M.Accurate interpolation with high-reso-lution time-variant Radon transforms[J].Geophysics,2002,67(2):644-656.
[8]Thorson R,Claerbout J.Velocity-stack and slant-stack stochasticinversion[J].Geophysics,1985,50(4):2727-2741.
[9]Darche G.Spatial interpolation using a fast parabolic Radon trans-form[C]//60th Annual Internat Mtg Soc Expl Geophys,Expanded abstracts,1990:1647-1650.
[2]Kabir M M N,Verschuur D J.Restoration of missing offsets by par-abolic Radon Transform[J].Geophysical Prospecting,1995,43:347-368.
[3]黄新武,吴律,牛滨华.基于抛物线拉东变换的地震道重构[J].中国矿业大学学报,2003,32(5):534-539.
[4]王维红,裴江云,张剑锋.加权抛物Radon变换叠前地震数据重建[J].地球物理学报,2007,50(3):851-859.
[5]Hampson D.Inverse velocity stacking for multiple elimination[J].Journal of the Canadian Society of Exploration geophysicists,1986,22:44-55.
[6]Kostov C.Toeplitz structure in slant-stack inversion:60th AnnualInternat[C]//60th Annual Internat Mtg Soc Expl Geophys,Ex-panded abstracts,1990:1618-1621.
[7]Trad D,Ulrych J,Sacchi M.Accurate interpolation with high-reso-lution time-variant Radon transforms[J].Geophysics,2002,67(2):644-656.
[8]Thorson R,Claerbout J.Velocity-stack and slant-stack stochasticinversion[J].Geophysics,1985,50(4):2727-2741.
[9]Darche G.Spatial interpolation using a fast parabolic Radon trans-form[C]//60th Annual Internat Mtg Soc Expl Geophys,Expanded abstracts,1990:1647-1650.
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